US7991151B2 - Method for secure delegation of calculation of a bilinear application - Google Patents
Method for secure delegation of calculation of a bilinear application Download PDFInfo
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- US7991151B2 US7991151B2 US11/667,031 US66703105A US7991151B2 US 7991151 B2 US7991151 B2 US 7991151B2 US 66703105 A US66703105 A US 66703105A US 7991151 B2 US7991151 B2 US 7991151B2
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Classifications
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
- H04L9/3073—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/56—Financial cryptography, e.g. electronic payment or e-cash
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/80—Wireless
Definitions
- the present invention relates to a method of securely delegating the calculation of a value f(X,Y) of a bilinear application to a computational server. It also relates to a method of securely verifying that a value f(X,Y) of a bilinear application is equal to a given value, and to a method of securely verifying that two values f(X,Y) and f(Z,T) of a bilinear application are equal.
- the invention relates very generally to the field of cryptography and more precisely to cryptographic methods of providing protection against fraud to a medium such as an electronic chip in transactions between a chip and a banking application or an electronic chip of a mobile telephone SIM card.
- the invention finds a particularly advantageous application in the use of new cryptographic methods deemed at present to be too costly in computation time, such as methods using bilinear functions.
- microchip cards are liable to suffer different types of fraud.
- a first type of fraud consists in duplicating the card without authorization, the term “cloning” often being used to characterize this operation.
- a second type of fraud consists in modifying the data attached to a card, in particular the amount of credit written in the memory of the card.
- Cryptography is used to combat these types of fraud, both to authenticate the card by means of an authentication algorithm and/or to authenticate the data by means of a digital signature, and also, where appropriate, to ensure the confidentiality of the data by means of encryption.
- Cryptography employs two entities which, for authentication, consist in a verifier entity and in an object to be authenticated.
- the cryptography may be either symmetrical or asymmetrical.
- the first authentication mechanisms to be developed for symmetrical cryptography consist in calculating once and for all an authentication value that is different for each card, storing it in the memory of the card, reading it on each transaction, and verifying it by interrogating an application of the network supporting the transaction in which authentication values that have already been assigned are either stored or recalculated.
- those mechanisms provide insufficient protection because the authentication value can be intercepted, reproduced, and replayed fraudulently as it is always the same for a given card, thus enabling a clone of the card to be produced.
- passive card authentication mechanisms are replaced by active authentication mechanisms that can also ensure the integrity of the data.
- the general principle of symmetrical active authentication mechanisms is as follows: at the time of authentication, the electronic chip and the application calculate an authentication value that is the result of applying a function to a list of arguments determined for each authentication. That list of arguments may include a random challenge defined by the application on each authentication, data contained in the electronic chip, and a secret key known to the electronic chip and the application. If the authentication value calculated by the electronic chip is identical to the authentication value calculated by the application, the electronic chip is deemed to be authentic and the transaction between the chip and the application is authorized.
- secret key mechanisms require the verification devices for authenticating the chip, such as those present in a public telephone network, an electronic payment terminal, or a public transport turnstile, to know the secret key held by said chip.
- said device if said device is required to be able to authenticate any chip issued in relation to the application, it must either store the secret keys of all the chips, or else it must store a base key for working out the secret key of any chip, known as a mother key or master key. Either way, each device stores sufficient information to be able to work out the secret keys of all the chips issued and therefore stores sufficient information to be able to clone any of them. It follows that successful hacking of any of the verification devices would entirely destroy the security of the application.
- One object of the present invention is to enable effective integration of cryptographic methods based on the use of bilinear functions, ensuring a maximum degree of security compatible with the uses made thereof, and despite the difficulty linked to their calculation complexity.
- a method for securely delegating the calculation of a value f(X,Y) of a bilinear application to a computational server comprises the steps of:
- the method of the invention also secures the data exchanged and strengthens the confidence in the results obtained.
- said entity using the computational server may be either the entity to be authenticated or the verifier entity.
- the effect of embodiments of the invention is therefore to delegate to the server most of the calculations involving bilinear functions and to ensure that the results returned by said server are secure in the sense that the chances of a malicious person succeeding in stealing the identity of a person using their public key would remain very low unless they also know the associated private key and have complete control over the computational server.
- the delegation method according to an embodiment of the invention is advantageously applied to two particular situations.
- a first situation relates to a method of verifying that a value f(X,Y) of a bilinear application is equal to a given value u by securely delegating to a computational server, the method being noteworthy in that said method comprises the steps of:
- the following signature mechanism illustrates this method of verifying that a value of a bilinear application is equal to a given value.
- the verifier entity receiving the message knows the three numbers constituting the public key but does not know the private key.
- the signatory then sends the recipient of the message the pair of numbers ⁇ ,r ⁇ .
- the receiver can have the computational server carry out the corresponding calculation of the bilinear function once and for all.
- f(g 1 ,g 2 ) is equal to a given known number u .
- the verification mechanism therefore involves the server calculating the quantity f( ⁇ ,g 2 m v r ).
- the verifier entity here the recipient of the message, chooses two numbers a and b , calculates ⁇ a and g 2 bm v br and sends them to the server, which sends back the value f( ⁇ a ,g 2 bm v br ), which by definition has the value f( ⁇ ,g 2 m v r ) ab.
- the verifier entity must calculate three values, such as: ⁇ a , g 2 bm v br , and u ab .
- one of the parameters a or b may be made equal to 1.
- a second application of the calculation delegation method provides a method of verifying that two values f(X,Y) and f(Z,T) of a bilinear application are equal by securely delegating calculation to a computational server, which method is noteworthy, in accordance with the invention, in that it comprises the following steps:
- the following signature mechanism gives an illustrative example of this method of securely verifying that two values of a bilinear application are equal.
- the signatory has a hashing function h which associates an element h(m) of the group G with the message m , this hashing function being shared with the recipient responsible for authenticating the message m .
- the verifier entity delegates the calculation of each member of the above equation to the computational server in the following manner.
- the verifier entity must calculate six values, namely ⁇ a , g b , h(m) c and v d , as well as [f( ⁇ a ,g b )] cd and [f(h(m) c ,v d )] ab .
- Another aspect of the invention is directed to a medium storing a computer program for implementing the method according to the invention.
- an embodiment of the invention can advantageously be applied to protecting said medium against fraud, and more specifically to making transactions between an electronic chip and a banking application secure and to making the electronic chip of a SIM card of a mobile telephone secure.
- said medium may be integrated into the mobile telephone.
Abstract
Description
f(g 1 a ,g 2 b)=[f(g 1 , g 2)]ab.
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- choosing two secret parameters a and b;
- calculating the numbers Xa and Yb;
- supplying the two numbers Xa and Yb to the computational server;
- said computational server calculating f(Xa,Yb);
- receiving the value of f(Xa,Yb) from the computational server; and
- extracting the abth root of f(Xa,Yb).
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- choosing two secret parameters a and b;
- calculating the numbers Xa and Yb;
- supplying the two numbers Xa and Yb to the computational server;
- said computational server calculating f(Xa,Yb);
- receiving the value of f(Xa,Yb) from the computational server; and
- comparing the value of f(Xa,Yb)p to the number uq, the numbers p and q satisfying the equation abp=q.
σ=g 1exp(m+rx)−1.
f(σ,g 2 m v r)=f(g 1 ,g 2)
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- choosing four secret parameters a, b, c and d;
- calculating the numbers Xa, Yb, Zc, and Td;
- supplying the four numbers Xa, Yb, Zc, and Td to the computational server;
- said computational server calculating f(Xa,Yb) and f(Zc,Td);
- receiving the values of f(Xa,Yb) and f(Zc,Td) from the computational server; and
- comparing the values of [f(Xa,Yb)]p and [f(Zc,Td)]q, the numbers p and q satisfying the equation abp=cdq.
f(σ,g)=f(h(m),v).
[f(σa ,g b)]cd =[f(h(m)c ,v d)]ab
or, more generally, with abp=cdq, the equation:
[f(σa ,g b)]p =[f(h(m)c ,v d)]q.
Claims (15)
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0411777 | 2004-11-04 | ||
FR0411777A FR2877453A1 (en) | 2004-11-04 | 2004-11-04 | SECURE DELEGATION METHOD OF CALCULATING A BILINE APPLICATION |
PCT/FR2005/002633 WO2006048524A1 (en) | 2004-11-04 | 2005-10-21 | Method for secure delegation of calculation of a bilinear application |
Publications (2)
Publication Number | Publication Date |
---|---|
US20070260882A1 US20070260882A1 (en) | 2007-11-08 |
US7991151B2 true US7991151B2 (en) | 2011-08-02 |
Family
ID=34952517
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US11/667,031 Active 2028-09-18 US7991151B2 (en) | 2004-11-04 | 2005-10-21 | Method for secure delegation of calculation of a bilinear application |
Country Status (5)
Country | Link |
---|---|
US (1) | US7991151B2 (en) |
EP (1) | EP1807967B1 (en) |
JP (1) | JP4740253B2 (en) |
FR (1) | FR2877453A1 (en) |
WO (1) | WO2006048524A1 (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US9049023B2 (en) | 2011-05-24 | 2015-06-02 | Zeutro Llc | Outsourcing the decryption of functional encryption ciphertexts |
US10361841B2 (en) * | 2010-10-26 | 2019-07-23 | Nippon Telegraph And Telephone Corporation | Proxy computing system, computing apparatus, capability providing apparatus, proxy computing method, capability providing method, program, and recording medium |
Families Citing this family (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
GB2407948B (en) * | 2003-11-08 | 2006-06-21 | Hewlett Packard Development Co | Smartcard with cryptographic functionality and method and system for using such cards |
JP5161177B2 (en) * | 2009-09-04 | 2013-03-13 | 日本電信電話株式会社 | Proxy calculation request device, proxy calculation request method, proxy calculation request program, recording medium |
KR101344352B1 (en) * | 2010-01-12 | 2013-12-24 | 니뽄 덴신 덴와 가부시키가이샤 | Proxy calculation system, proxy calculation method, proxy calculation requesting apparatus, and proxy calculation program and recording medium therefor |
JP5480763B2 (en) * | 2010-09-21 | 2014-04-23 | 日本電信電話株式会社 | Decryption system, general-purpose terminal, high-reliability terminal, key generation device, decryption method, program |
JP5506633B2 (en) * | 2010-11-04 | 2014-05-28 | 日本電信電話株式会社 | Proxy calculation system, terminal device, proxy calculation device, proxy calculation method, and program |
JP5427195B2 (en) * | 2011-01-14 | 2014-02-26 | 日本電信電話株式会社 | Proxy calculation system, method, request device, calculation device, program |
US9542155B2 (en) * | 2011-03-04 | 2017-01-10 | Nippon Telegraph And Telephone Corporation | Proxy calculation system, method, request device and program thereof |
WO2014112523A1 (en) * | 2013-01-16 | 2014-07-24 | 日本電信電話株式会社 | Decryption-service provision device, processing device, safety evaluation device, program, and recording medium |
Citations (9)
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EP0381523A2 (en) | 1989-02-02 | 1990-08-08 | Kabushiki Kaisha Toshiba | Server-aided computation method and distributed information processing unit |
US5369708A (en) | 1992-03-31 | 1994-11-29 | Kabushiki Kaisha Toshiba | Fast server-aided computation system and method for modular exponentiation without revealing client's secret to auxiliary device |
US20030161472A1 (en) | 2002-02-27 | 2003-08-28 | Tong Chi Hung | Server-assisted public-key cryptographic method |
US20030177350A1 (en) * | 2002-03-16 | 2003-09-18 | Kyung-Hee Lee | Method of controlling network access in wireless environment and recording medium therefor |
US20030182554A1 (en) | 2002-03-21 | 2003-09-25 | Gentry Craig B. | Authenticated ID-based cryptosystem with no key escrow |
US20040139029A1 (en) * | 2002-12-24 | 2004-07-15 | Information And Communications University Educational Foundation | Apparatus and method for generating and verifying ID-based blind signature by using bilinear parings |
US6779111B1 (en) | 1999-05-10 | 2004-08-17 | Telefonaktiebolaget Lm Ericsson (Publ) | Indirect public-key encryption |
US7113594B2 (en) * | 2001-08-13 | 2006-09-26 | The Board Of Trustees Of The Leland Stanford University | Systems and methods for identity-based encryption and related cryptographic techniques |
US7590236B1 (en) * | 2004-06-04 | 2009-09-15 | Voltage Security, Inc. | Identity-based-encryption system |
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JPH0372737A (en) * | 1989-05-31 | 1991-03-27 | Toshiba Corp | Request calculation system |
JP3137190B2 (en) * | 1989-02-02 | 2001-02-19 | 株式会社東芝 | Message conversion method |
JPH0619393A (en) * | 1992-03-31 | 1994-01-28 | Toshiba Corp | Request calculating device |
FR2792789B1 (en) * | 1999-04-20 | 2001-08-31 | Bull Cp8 | SIGNATURE VERIFICATION OR AUTHENTICATION PROCESS |
JP4450969B2 (en) * | 2000-05-02 | 2010-04-14 | 村田機械株式会社 | Key sharing system, secret key generation device, common key generation system, encryption communication method, encryption communication system, and recording medium |
JP2002164877A (en) * | 2000-09-14 | 2002-06-07 | Advanced Mobile Telecommunications Security Technology Research Lab Co Ltd | Key escrow and group communication method |
-
2004
- 2004-11-04 FR FR0411777A patent/FR2877453A1/en active Pending
-
2005
- 2005-10-21 EP EP05811834.0A patent/EP1807967B1/en active Active
- 2005-10-21 US US11/667,031 patent/US7991151B2/en active Active
- 2005-10-21 WO PCT/FR2005/002633 patent/WO2006048524A1/en active Application Filing
- 2005-10-21 JP JP2007539603A patent/JP4740253B2/en active Active
Patent Citations (9)
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EP0381523A2 (en) | 1989-02-02 | 1990-08-08 | Kabushiki Kaisha Toshiba | Server-aided computation method and distributed information processing unit |
US5369708A (en) | 1992-03-31 | 1994-11-29 | Kabushiki Kaisha Toshiba | Fast server-aided computation system and method for modular exponentiation without revealing client's secret to auxiliary device |
US6779111B1 (en) | 1999-05-10 | 2004-08-17 | Telefonaktiebolaget Lm Ericsson (Publ) | Indirect public-key encryption |
US7113594B2 (en) * | 2001-08-13 | 2006-09-26 | The Board Of Trustees Of The Leland Stanford University | Systems and methods for identity-based encryption and related cryptographic techniques |
US20030161472A1 (en) | 2002-02-27 | 2003-08-28 | Tong Chi Hung | Server-assisted public-key cryptographic method |
US20030177350A1 (en) * | 2002-03-16 | 2003-09-18 | Kyung-Hee Lee | Method of controlling network access in wireless environment and recording medium therefor |
US20030182554A1 (en) | 2002-03-21 | 2003-09-25 | Gentry Craig B. | Authenticated ID-based cryptosystem with no key escrow |
US20040139029A1 (en) * | 2002-12-24 | 2004-07-15 | Information And Communications University Educational Foundation | Apparatus and method for generating and verifying ID-based blind signature by using bilinear parings |
US7590236B1 (en) * | 2004-06-04 | 2009-09-15 | Voltage Security, Inc. | Identity-based-encryption system |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
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US10361841B2 (en) * | 2010-10-26 | 2019-07-23 | Nippon Telegraph And Telephone Corporation | Proxy computing system, computing apparatus, capability providing apparatus, proxy computing method, capability providing method, program, and recording medium |
US9049023B2 (en) | 2011-05-24 | 2015-06-02 | Zeutro Llc | Outsourcing the decryption of functional encryption ciphertexts |
Also Published As
Publication number | Publication date |
---|---|
EP1807967A1 (en) | 2007-07-18 |
FR2877453A1 (en) | 2006-05-05 |
EP1807967B1 (en) | 2019-09-04 |
WO2006048524A1 (en) | 2006-05-11 |
JP2008519303A (en) | 2008-06-05 |
JP4740253B2 (en) | 2011-08-03 |
US20070260882A1 (en) | 2007-11-08 |
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